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4 years ago

7

Write 2^40 as an exponent with a base of: a 2^2; b 2^5; c 2^8; 2^10

1 answer:

MA_775_DIABLO [31]4 years ago

6 0

Answer:

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

Exact Form: a = 6, 2 3

Decimal Form: a = 6 , 0. ¯ 6

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Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below cer

aleksley [76]

Answer:

a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that $p = 0.7$

Five residential subscribers are randomly selected from San Juan, Puerto Rico

This means that $n = 5$

a. All five qualify for the favorable rate

This is P(X = 5). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681$

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

This is

$P(X \geq 4) = P(X = 4) + P(X = 5)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602$

$P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681$

$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283$

0.5283 = 52.83% probability that at least four qualify for the favorable rates

5 0

3 years ago

The least common multiple of 3,4,6,8 is

kati45 [8]

The least common multiple is 2

5 0

3 years ago

Read 2 more answers

Andrew is evaluating his current financial position by totaling his monthly cash inflows and outflows. His cash inflows each mon

jeka57 [31]

Answer:

Andrew has $15 left over each month

Step-by-step explanation:

Inflows=$240+$60=$300/mo.

Outflows=$170+$70+45=$285/mo.

Inflows-Outflows=left over

$300-$285=$15

8 0

3 years ago

What is the perimeter?

Harlamova29_29 [7]

Answer:

80

Step-by-step explanation:

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3 years ago

Graph the quadratic function f(x)= -2x^2-3x+2

schepotkina [342]

Answer:

it would be the graph with the maximum (opening down) in the first photo with the top on the left side of the y axis

4 0

3 years ago